Write down the Gibbs sum. Be sure to get all of the indices correct.
Give the expression for the absolute probability that a system will be found in the state with N 1 particles and energy .
Give an expression for the average value of a property A for a system in diffusive and thermal contact with a "reservoir". A "reservoir" is a huge system next to our smaller system with large energy and number of particles.
Give an expression for the average number of particles in a system that is in thermal and diffusive contact with a reservoir.
We are looking for < N > , which we can calculate using the formula we just derived.
Suppose that we have a system that can be unoccupied or can have one particle in a state with energy . Write the Gibbs sum for this system.
One possible state has N = 0 , for which we say that the energy is also zero. So the first term in the sum is 1 . The second possible state has N = 1 , and energy . We can write the total sum as:
We sometimes simplify this by defining λâÉáe μ/τ , in which case the answer can be written more simply as Z G = 1 + λe -/τ .
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